6 papers
A dimension-free bound for isoperimetry of unconditional log-concave measures
Dan Mikulincer, Ilias Zadik
We prove a dimension-free Poincaré inequality for isotropic unconditional log-concave probability measures, establishing the Kannan-Lovász-Simonovits (KLS) conjecture in the uncond…
Geometric obstructions to Lipschitz transport between weighted Hessian manifolds
William Dudarov, Dan Mikulincer
We construct a weighted Riemannian manifold satisfying , the curvature-dimension condition, with the following property: if denotes…
Dimension-free Gaussian tail estimates for linear functionals on convex bodies
Brayden Letwin, Dan Mikulincer
Let be a centered convex body of volume one. We prove that there exist absolute constants and an orthonormal set of vectors wi…
The Benefits of Temporal Correlations: SGD Learns k-Juntas from Random Walks Efficiently
Elisabetta Cornacchia, Dan Mikulincer, Elchanan Mossel
We study how temporal correlations in the data can make certain sparse learning problems efficiently learnable by gradient-based methods. Our focus is on Boolean k-juntas, a canoni…
Anti-concentration of polynomials: balls and symmetric measures
Itay Glazer, Dan Mikulincer
We begin with the observation, based on previous results, that dimension-free lower bounds on the variance of a polynomial under a log-concave measure yield dimension-free small-ba…
Fast mixing in Ising models with a negative spectral outlier via Gaussian approximation
Dan Mikulincer, Youngtak Sohn
We study the mixing time of Glauber dynamics for Ising models in which the interaction matrix contains a single negative spectral outlier. This class includes the anti-ferromagneti…